phit

Data & Workflow

Statistics, Modeling, & Visualization

Statistics and optimization functions

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Descriptive statistics, density estimation, interpolation, the ECDF, and one-dimensional optimization. Missing values, weights, and errors follow the shared rules.

Summaries

stat_mean()

Arithmetic mean.

  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_mean(    array $values,    string $missing = 'raise',): float
Parameter Type Default Description
$values array required Data; null and NAN are missing
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns float

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

stat_median()

Median: the type 7 quantile at 0.5.

  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_median(    array $values,    string $missing = 'raise',): float
Parameter Type Default Description
$values array required Data; null and NAN are missing
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns float

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

stat_var()

Variance: type: 'sample' divides by n − 1, and 'population' by n.

  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_var(    array $values,    string $type = 'sample',    string $missing = 'raise',): float
Parameter Type Default Description
$values array required Data; null and NAN are missing
$type string 'sample' 'sample' divides by n − 1, 'population' by n
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns float

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

stat_sd()

Standard deviation: the square root of stat_var().

  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_sd(    array $values,    string $type = 'sample',    string $missing = 'raise',): float
Parameter Type Default Description
$values array required Data; null and NAN are missing
$type string 'sample' 'sample' divides by n − 1, 'population' by n
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns float

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

stat_quantile()

Sample quantile by R’s default type 7, linear interpolation.

  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_quantile(    array $values,    float $p,    string $missing = 'raise',): float
Parameter Type Default Description
$values array required Data; null and NAN are missing
$p float required Probability in [0, 1]
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns float

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

stat_quantile_array()

Several type 7 quantiles from one sort.

  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_quantile_array(    array $values,    array $probabilities,    string $missing = 'raise',): array
Parameter Type Default Description
$values array required Data; null and NAN are missing
$probabilities array required Probabilities in [0, 1]
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns list<float>

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

stat_weighted_mean()

Weighted mean: sum(w·x) / sum(w).

  • Weights must be nonnegative with a positive sum. A negative weight is rejected before missing values are removed.
  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_weighted_mean(    array $values,    array $weights,    string $missing = 'raise',): float
Parameter Type Default Description
$values array required Data; null and NAN are missing
$weights array required Nonnegative weights with a positive sum, aligned with the values
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns float

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

stat_weighted_var()

Weighted variance: type: 'frequency' divides by W − 1, 'reliability' by W − sum(w²)/W, and 'population' by W, with W = sum(w).

  • A negative weight is rejected before missing values are removed.
  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_weighted_var(    array $values,    array $weights,    string $type = 'frequency',    string $missing = 'raise',): float
Parameter Type Default Description
$values array required Data; null and NAN are missing
$weights array required Nonnegative weights with a positive sum, aligned with the values
$type string 'frequency' 'frequency' divides by W − 1, 'reliability' by W − sum(w²)/W, 'population' by W, with W = sum(w)
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns float

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

stat_cov()

Covariance of two aligned arrays: type: 'sample' divides by n − 1, and 'population' by n.

  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_cov(    array $x,    array $y,    string $type = 'sample',    string $missing = 'raise',): float
Parameter Type Default Description
$x array required Data; null and NAN are missing
$y array required Second variable, aligned with the first; null and NAN are missing
$type string 'sample' 'sample' divides by n − 1, 'population' by n
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns float

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

stat_cor()

Pearson correlation of two aligned arrays.

  • Returns NAN when either input is constant.
  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_cor(    array $x,    array $y,    string $missing = 'raise',): float
Parameter Type Default Description
$x array required Data; null and NAN are missing
$y array required Second variable, aligned with the first; null and NAN are missing
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns float

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

Smoothing and interpolation

stat_density()

Kernel density estimate, like R’s density().

  • Bins the data linearly, convolves with the kernel by FFT, and interpolates onto n points from from to to.
  • bw is nrd0, nrd, or a positive number, multiplied by adjust.
  • Weights are used as given; as in R, weights that sum to one are renormalized after missing values are removed.
  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_density(    array $x,    string|float $bw = 'nrd0',    float $adjust = 1.0,    string $kernel = 'gaussian',    int $n = 512,    ?float $from = NULL,    ?float $to = NULL,    float $cut = 3.0,    ?array $weights = NULL,    string $missing = 'raise',): array
Parameter Type Default Description
$x array required Data; null and NAN are missing
$bw string\|float 'nrd0' 'nrd0', 'nrd', or a positive bandwidth
$adjust float 1.0 Multiplier applied to the bandwidth
$kernel string 'gaussian' 'gaussian', 'epanechnikov', 'rectangular', 'triangular', 'biweight', 'cosine', or 'optcosine'
$n int 512 Number of output points
$from ?float NULL Left end of the output grid; null extends the data range by cut bandwidths
$to ?float NULL Right end of the output grid; null extends the data range by cut bandwidths
$cut float 3.0 Bandwidths beyond the data range for the default grid
$weights ?array NULL Nonnegative weights aligned with x, used as given; null weights all points equally
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns array{x: list<float>, y: list<float>, bw: float, n: int}

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

stat_bw_nrd0()

Silverman’s rule-of-thumb bandwidth, like R’s bw.nrd0(): 0.9 · min(sd, IQR/1.34) · n^(−1/5), with R’s fallbacks when that is zero.

  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_bw_nrd0(    array $x,    string $missing = 'raise',): float
Parameter Type Default Description
$x array required Data; null and NAN are missing
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns float

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

stat_bw_nrd()

Scott’s variation of the rule-of-thumb bandwidth, like R’s bw.nrd(): 1.06 · min(sd, IQR/1.34) · n^(−1/5).

  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_bw_nrd(    array $x,    string $missing = 'raise',): float
Parameter Type Default Description
$x array required Data; null and NAN are missing
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns float

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

stat_approx()

Interpolates the points (x, y) at xout, like R’s approx().

  • method: 'linear' interpolates linearly; 'constant' uses a step function in which f weights the right-hand value.
  • Outside [min(x), max(x)], rule: 1 returns NAN and rule: 2 the value at the nearer end.
  • Tied x values collapse by ties: 'mean', 'min', or 'max'.
  • A null or NAN in xout returns NAN.
  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_approx(    array $x,    array $y,    array $xout,    string $method = 'linear',    int $rule = 1,    string $ties = 'mean',    float $f = 0.0,    string $missing = 'raise',): array
Parameter Type Default Description
$x array required Abscissae of the points; null and NAN are missing
$y array required Ordinates, aligned with x; null and NAN are missing
$xout array required Evaluation points; null or NAN gives NAN
$method string 'linear' 'linear' or 'constant'
$rule int 1 1 returns NAN outside the data range; 2 returns the value at the nearer end
$ties string 'mean' 'mean', 'min', or 'max' for tied x values
$f float 0.0 For method 'constant', the weight of the right-hand value, in [0, 1]
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns list<float>

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

stat_ecdf()

Empirical CDF of x at each q: the proportion of x at or below q, as R’s ecdf(x)(q).

  • A null or NAN in q returns NAN.
  • null and NAN are missing: missing: 'raise' rejects them, and missing: 'drop' removes them, pairwise for two arrays.
  • Infinite input, or arithmetic that overflows, throws.
Phit\stat_ecdf(    array $x,    array $q,    string $missing = 'raise',): array
Parameter Type Default Description
$x array required Data; null and NAN are missing
$q array required Evaluation points; null or NAN gives NAN
$missing string 'raise' 'raise' rejects null and NAN; 'drop' removes them, pairwise for aligned inputs

Returns list<float>

Errors Exception: code 1001, 1002, or 1003 for an input error.

See also Details

Optimization and root finding

optimize()

Minimizes f on [lower, upper], or maximizes it with maximum: true, like R’s optimize().

  • Uses Brent’s golden-section and parabolic search, step for step as R does.
  • Returns minimum (or maximum) and objective, the value of f there.
  • f takes one float and returns an int or float. An exception thrown by f propagates.
  • A nonfinite value during the search is replaced by the largest finite value, as in R, with one warning.
Phit\optimize(    callable $f,    float $lower,    float $upper,    ?float $tol = NULL,    bool $maximum = false,): array
Parameter Type Default Description
$f callable required Objective: takes one float and returns an int or float
$lower float required Lower end of the search interval
$upper float required Upper end of the search interval
$tol ?float NULL Default PHP_FLOAT_EPSILON ** 0.25, as R
$maximum bool false Maximize instead of minimize

Returns array{minimum: float, objective: float}\|array{maximum: float, objective: float}

Errors Exception: code 1001 for an input error.

See also Details

uniroot()

Finds a root of f in [lower, upper], like R’s uniroot().

  • Uses Brent’s method, step for step as R does. f(lower) and f(upper) must not have the same sign.
  • Returns root, f_root, iter, and estim_prec. When it runs out of iterations it warns, sets iter to maxiter, and returns its last estimate.
  • f takes one float and returns an int or float. An exception thrown by f propagates.
  • A nonfinite value during the search is replaced by the largest finite value, as in R, with one warning.
Phit\uniroot(    callable $f,    float $lower,    float $upper,    ?float $tol = NULL,    int $maxiter = 1000,): array
Parameter Type Default Description
$f callable required Function whose root is sought: takes one float and returns an int or float
$lower float required Lower end of the search interval
$upper float required Upper end of the search interval
$tol ?float NULL Default PHP_FLOAT_EPSILON ** 0.25, as R
$maxiter int 1000 Largest number of iterations

Returns array{root: float, f_root: float, iter: int, estim_prec: float}

Errors Exception: code 1001 for an input error.

See also Details